x^2+4x-18=240

Solution for x^2+4x-18=240 equation:

x^2+4x-18=240

We move all terms to the left:

x^2+4x-18-(240)=0

We add all the numbers together, and all the variables

x^2+4x-258=0

a = 1; b = 4; c = -258;
Δ = b2-4ac
Δ = 42-4·1·(-258)
Δ = 1048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1048}=\sqrt{4*262}=\sqrt{4}*\sqrt{262}=2\sqrt{262}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{262}}{2*1}=\frac{-4-2\sqrt{262}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{262}}{2*1}=\frac{-4+2\sqrt{262}}{2}
$